You're sitting there with the digital clock ticking down on Bluebook. Your palms are probably a little sweaty. You see a geometry problem involving a circle, and your brain just... freezes. We’ve all been there. The thing is, the College Board gives you a reference sheet, but if you're actually clicking back and forth to look at it, you're losing. You're hemorrhaging time.
Knowing the formulas to know for the SAT isn't just about memorization; it's about speed. It’s about recognizing a pattern before your conscious mind even finishes reading the prompt. Since the transition to the Digital SAT (DSAT), the math has become more logic-heavy and less about "gotcha" arithmetic. But if you don't have the foundational tools burned into your skull, Desmos won't save you.
The stuff they give you (and why you should ignore it)
The reference sheet is a security blanket. It’s got the area of a circle, the volume of a right cone, and the Pythagorean theorem. Honestly, if you have to look up $a^2 + b^2 = c^2$, we need to have a serious talk about your prep strategy.
The real danger is the time tax. Every time you open that reference window, you lose about five to ten seconds of cognitive flow. In a test where the second module can get notoriously "wordy" and complex, those seconds are gold. You need to know the basics—area, volume, basic trig—so well that they feel like breathing.
The linear equation obsession
The SAT loves lines. It's obsessed with them. You'll see slope-intercept form ($y = mx + b$) more than almost anything else. But the test writers are sneaky. They’ll give you a word problem about a plumber charging a flat fee plus an hourly rate.
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The "b" is your starting point—the flat fee. The "m" is your rate of change.
Sometimes they’ll give you two points and ask for the equation. You could use the slope formula, which is basically just the change in $y$ over the change in $x$:
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
But here is a pro tip: use the Desmos calculator. If you have two points, type them into a table and run a linear regression. It’s faster. It’s more accurate. It’s basically legal cheating. However, you still need to understand what the slope means in context. If the slope is negative, the plumber is losing money, or maybe the water level in a tank is dropping. Context is everything on the DSAT.
Standard Form and the Intercept Trick
Then there’s standard form: $Ax + By = C$.
Most students immediately try to rewrite this into $y = mx + b$. Don't do that. It’s a waste of time. If you need the x-intercept, set $y$ to zero. If you need the y-intercept, set $x$ to zero. To find the slope directly from standard form, just use $-A/B$. It takes half a second.
Quadratics: The heavy hitters
If lines are the bread and butter, quadratics are the main course. You’re going to see parabolas. You’re going to see them a lot.
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The vertex form, $y = a(x - h)^2 + k$, is your best friend because it literally tells you the highest or lowest point of the graph $(h, k)$. If a question asks for the maximum value of a ball thrown in the air, they are asking for $k$.
Then you have the quadratic formula. You know the one.
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
But wait. Do you actually need to solve for $x$? Usually, no. The SAT loves the discriminant. That’s the part under the square root: $b^2 - 4ac$.
- If it’s positive, you have two real solutions (the graph hits the x-axis twice).
- If it’s zero, you have one solution (the vertex is on the x-axis).
- If it’s negative, you have no real solutions (the graph is floating in space).
I’ve seen dozens of problems that can be solved in ten seconds just by checking the discriminant instead of doing the whole formula. It’s a massive time-saver.
Sum and Product of Roots
This is a "high-level" secret that isn't on the reference sheet. If you have a quadratic $ax^2 + bx + c = 0$, the sum of the roots is always $-b/a$. The product of the roots is always $c/a$.
Imagine a question asks: "What is the sum of the solutions to $3x^2 - 12x + 5 = 0$?"
You could use the quadratic formula, get two messy decimals, and add them. Or you could just look at it and say $12/3 = 4$. Boom. Done. Next question.
Percentages and exponential growth
Percentages on the SAT aren't just about calculating a tip at a restaurant. They are usually about "percent change" or exponential growth.
The basic formula for exponential growth is $A = P(1 + r)^t$.
- $P$ is your initial amount.
- $r$ is your rate (as a decimal!).
- $t$ is time.
If a population is growing by 5%, your multiplier is $1.05$. If it’s shrinking by 5%, your multiplier is $0.95$.
One thing that trips people up is the "compound interest" variation. If it compounds monthly, you divide the rate by 12 and multiply the time by 12. It’s a small detail, but it’s the difference between a 750 and an 800 on the math section.
Geometry and the circle equation
Geometry has been scaled back on the digital version, but it still bites. Specifically, the equation of a circle.
$$(x - h)^2 + (y - k)^2 = r^2$$
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The center is $(h, k)$ and the radius is $r$. Watch out for the $r^2$. If the equation ends in $= 16$, the radius is 4, not 16. The SAT loves to put 16 as an answer choice just to catch you sleeping.
You also need to know your circle theorems. Like, the fact that a tangent line is always perpendicular to the radius at the point of tangency. Or the arc length formula.
Arc length is just a fraction of the circumference.
$$\text{Arc Length} = \frac{\theta}{360} \times 2\pi r$$
If you’re working in radians (and you should be comfortable with both), it’s even easier: $S = r\theta$.
Statistics and the "Margin of Error"
Statistics on the SAT are less about formulas and more about concepts, but there are a few things to keep in your back pocket.
- Mean vs. Median: If you add a huge outlier to a data set, the mean will change a lot, but the median will barely budge.
- Standard Deviation: You don't need to calculate it. You just need to know what it means. High standard deviation = data is spread out. Low standard deviation = data is clustered together.
- Margin of Error: If you want a smaller margin of error, you need a larger sample size. That’s a common conceptual question.
Trigonometry: SOH CAH TOA and beyond
Trig is usually limited to right triangles.
- Sine = Opposite / Hypotenuse
- Cosine = Adjacent / Hypotenuse
- Tangent = Opposite / Adjacent
But here’s the one that catches people: $\sin(x) = \cos(90 - x)$.
In radians, that’s $\sin(x) = \cos(\pi/2 - x)$.
If the test tells you that $\sin(a) = 0.6$, and asks what $\cos(b)$ is for the other acute angle in the triangle, the answer is $0.6$. It's a "blink and you'll miss it" kind of concept.
How to actually practice this
Don't just stare at a list of formulas to know for the SAT. That's useless. Passive learning is a myth.
- Flashcards for the "Unlisted" Formulas: Put the sum/product of roots, the discriminant, and the circle equation on cards. Quiz yourself while you're on the bus or waiting for lunch.
- Desmos Mastery: Open the Desmos SAT calculator (the one actually built into Bluebook) and practice graphing these formulas. Learn how to find a vertex just by clicking the curve.
- Drill by Category: Use Khan Academy or a prep book to do 20 problems in a row that only deal with quadratics. You need to see how the same formula can be disguised in five different ways.
- Timed Mini-Sections: Give yourself 10 minutes to do 8 "hard" math questions. This forces you to rely on the formulas for speed rather than grinding out the long way.
Moving forward with your prep
The SAT isn't a math test; it's a "how well do you know the SAT" test. The math is just the medium. By internalizing these formulas, you free up your brain to handle the logic and the reading comprehension part of the math problems.
Start by taking a full-length practice test on Bluebook. Don't look at the reference sheet once. Note every time you felt the urge to check it—those are the formulas you haven't mastered yet. Focus your study sessions specifically on those gaps. Once you can recall the vertex form or the sum of roots instantly, you'll find yourself finishing the math modules with minutes to spare, which is the best feeling in the world when you're aiming for a top score.
Actionable Next Steps
- Download the Bluebook App: If you haven't taken a practice test yet, do it today to see your baseline.
- Master Desmos: Spend 30 minutes learning how to use the "Regressions" feature ($y_1 \sim mx_1 + b$) for linear and quadratic data.
- Memorize the "Invisible" Formulas: Specifically the sum/product of roots and the discriminant, as these are not provided on the test's reference sheet.
- Check Your Radians: Ensure you know how to switch between degrees and radians quickly in the calculator settings, as the SAT will jump between them constantly.